Decoding Of Non-binary LDPC Codes Research Articles

Dynamic Multi-Symbol Flipping Decoding of Non-Binary LDPC Codes

A dynamic multi-symbol (DM) flipping scheme is proposed for various symbol flipping decodings of non-binary low-density parity-check (NB-LDPC) codes. This new approach divides the whole decoding process into multiple stages according to the number of iterations and allows a different maximum number of symbols to be flipped in each stage. Numerical analysis reveals that the proposed multi-symbol flipping scheme can yield a higher probability of correct flipping with the dynamic flipping threshold. The proposed DM scheme can be highly parallelized, extensively improving the decoder throughput over existing symbol flipping decoding algorithms based on prediction (SFDP). Numerical results show that the DM scheme can significantly enhance the error correction capability and achieve faster convergence speed with little increase in average computational complexity.

A Stopping Criterion for Symbol Flipping Decoding of Non-Binary LDPC Codes

A Stopping Criterion for Symbol Flipping Decoding of Non-Binary LDPC Codes

Randomly Penalized Symbol Flipping Decoding of Non-Binary LDPC Codes

Symbol flipping decoding (SFD) of non-binary low-density parity-check (NB-LDPC) codes has lower implementation complexity at a cost of performance degradation, when compared with other belief propagation decoding algorithms. This paper proposes modified SFD algorithms based on prediction (SFDP) for NB-LDPC codes by introducing random penalty items into the flipping metrics. Two types of noise with uniform and Gaussian distributions are considered. A probabilistic analysis shows theoretically that the randomly penalized SFDP algorithms can be advantageous in the correct flipping probability over their original versions. Simulation results show that the proposed penalizing methods exhibit significant performance gains for both regular and irregular NB-LDPC codes with different rates and alphabet sizes in both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC).

Fast-Converging Flipping Rules for Symbol Flipping Decoding of Non-Binary LDPC Codes

Fast-Converging Flipping Rules for Symbol Flipping Decoding of Non-Binary LDPC Codes

Bit-Metric Decoding of Non-Binary LDPC Codes With Probabilistic Amplitude Shaping

A new approach for combining non-binary low-density parity-check (NB-LDPC) codes with higher-order modulation and probabilistic amplitude shaping (PAS) is presented. Instead of symbol-metric decoding (SMD), a bit-metric decoder (BMD) is used so that matching the field order of the non-binary code to the constellation size is not needed, which increases the flexibility of the coding scheme. Information rates, density evolution thresholds and finite-length simulations show that the flexibility comes at no loss of performance if PAS is used.

Improved Hard-Reliability Based Majority-Logic Decoding for Non-Binary LDPC Codes

This letter proposes two methods to improve the iterative hard-reliability based majority-logic decoding algorithm for non-binary low-density parity-check (NB-LDPC) codes. The first method improves the error-correcting performance by modifying the initialization process, which is based on the fact that Gray coded modulation is used in general. In addition, a storage reduction method is proposed to make the proposed decoding hardware-friendly, which reduces the memory size considerably while sustaining the error-correcting performance achieved by the modified initialization. For an NB-LDPC code over Galois field of 32 elements, the memory size is reduced by about 75% compared with that of the conventional decoding algorithm.

Bit-Reliability Based Low-Complexity Decoding Algorithms for Non-Binary LDPC Codes

This paper presents bit-reliability based majority-logic decoding (MLgD) algorithms for non-binary LDPC codes. The proposed algorithms pass only one Galois field element and its reliability along each edge of the Tanner graph of a non-binary LDPC code. Since their reliability updates are in terms of bits rather than symbols, they are more efficient than traditional MLgD based decoding algorithms. By weighting the soft reliability of the extrinsic information-sums based on their hard reliability, the proposed algorithms can achieve good error performance for non-binary LDPC codes with various column weights. Moreover, their computational complexity and memory consumption are remarkably reduced compared with existing MLgD based decoding algorithms. As a result, they provide effective tradeoffs between error performance and complexity for decoding of non-binary LDPC codes.

Parallel Symbol-Flipping Decoding for Non-Binary LDPC Codes

A new low-complexity parallel symbol-flipping decoding algorithm for non-binary low-density parity-check (NB-LDPC) codes is proposed. The algorithm outperforms quite a number of existing reliability-based message-passing algorithms, and its computation complexity is smaller than that of almost all the previously proposed iterative decoding algorithms for NB-LDPC codes. It is suitable for decoding NB-LDPC codes whose parity-check matrices have large column weights.

Efficient Stochastic Decoding of Non-Binary LDPC Codes with Degree-Two Variable Nodes

In this letter, we present an optimized version of the relaxed half-stochastic (RHS) algorithm targeted at non-binary LDPC codes with a variable node degree equal to two. The new algorithm has significantly fewer multiplications while maintaining an error-correction performance and a decoding iteration count identical to those of the original.

An Iterative LLR Derivation Algorithm Based on Extended Min-sum Decoding of Non-binary LDPC Codes

An Iterative LLR Derivation Algorithm Based on Extended Min-sum Decoding of Non-binary LDPC Codes

Some Results on MAP Decoding of Non-Binary LDPC Codes Over the BEC

In this paper, the transmission over the binary erasure channel (BEC) using non-binary LDPC (NBLDPC) codes is considered. The concept of peeling decoder and stopping sets is generalized to NBLDPC codes. Using these generalizations, a combinatorial characterization of decoding failures of NBLDPC codes is given, under assumption that the Belief Propagation (BP) decoder is used. Then, the residual ensemble of codes resulted by the BP decoder is defined and the design rate and the expectation of total number of codewords of the residual ensemble are computed. The decoding failure criterion combined with the density evolution analysis helps us to compute the asymptotic residual degree distribution for NBLDPC codes. Our approach to compute the residual degree distribution on the check node side is not efficient as it is based on enumeration of all the possible connections on the check node side which satisfy the decoding failure criterion. So, the computation of the asymptotic check node side residual degree distribution and further part of our analysis is performed for NBLDPC codes over GF2m with m = 2 . In order to show that asymptotically almost every code in such LDPC ensemble has a rate equal to the design rate, we generalize the argument of the Maxwell construction to NBLDPC codes, defined over GF22. It is also observed that, like in the binary setting, the Maxwell construction, relating the performance of MAP and BP decoding holds in this setting.

Low-complexity decoding for non-binary LDPC codes in high order fields

In this paper, we propose a new implementation of the Extended Min-Sum (EMS) decoder for non-binary LDPC codes. A particularity of the new algorithm is that it takes into accounts the memory problem of the non-binary LDPC decoders, together with a significant complexity reduction per decoding iteration. The key feature of our decoder is to truncate the vector messages of the decoder to a limited number nm of values in order to reduce the memory requirements. Using the truncated messages, we propose an efficient implementation of the EMS decoder which reduces the order of complexity to ?(nm log2 nm). This complexity starts to be reasonable enough to compete with binary decoders. The performance of the low complexity algorithm with proper compensation is quite good with respect to the important complexity reduction, which is shown both with a simulated density evolution approach and actual simulations.